Scale setting of SU ( N ) Yang–Mills theory, topology and large- N volume independence

We set the scale of SU ( N ) Yang-Mills theories for N = 3 , 5, 8 and in the large- N limit via gradient flow, as a first step towards the computation of the large- N Λ -parameter using step scaling. We adopt twisted boundary conditions to achieve large- N volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼ 0.025 fm for all the explored values of N , a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large- N twisted volume reduction.